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Variational discontinuous Galerkin method in broken Sobolev spaces and application to the Gamma-convergence of Helfrich-type energies

Meyer, Haroun
(2025)

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Meyer_54611800_2025.pdf
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Details

Supervisors
Olbermann, Heiner
Faculty
Faculté des sciences
Degree label
Master [120] en sciences mathématiques, à finalité approfondie
Abstract
We establish results in broken Sobolev spaces analogous to the ones in classical Sobolev spaces. For example, we extend the trace theorem, compact embeddings, or estimates such as the Poincaré inequality. This theoretical basis then serves to prove the Gamma-convergence of functionals discretised through the variational discontinuous Galerkin method. An application of these results is then discussed: we prove that a certain discretisation of Helfrich-type energies is consistent and convergent by Gamma-convergence.